Authors:

Lauren Lazarus
(University of New Hampshire)

Joseph Tranquillo
(Bucknell University)

Many physical systems are composed of multiple oscillators which
when coupled tend to synchronize. In many systems, coupling is
assumed to be bidirectional and diffusive, which in phase space
acts to strongly attract limit cycles to one another. Our
simulations explore the impact of other forms of coupling, such
as synaptic, phase and transient coupling which also occur in
physical systems and can have a profound impact on system
dynamics. For example, when we transformed two unit oscillator
into Cartesian coordinates and coupled only one state variable,
the limit cycles collapsed to equilibrium points. We have also
found bifurcation routes to and from limit cycles when the
FitzHugh-Nagumo and Hindmarsh-Rose neuron models were coupled via
unidirectional synapses which do not occur when the cells are
coupled diffusively. The underlying reason for these differences
is that non-diffusive coupling may be alternately attractive and
repulsive at various phases of the limit cycles. These results
suggest that the type of coupling can be just as important in
determining system behavior as the dynamics of the individual
oscillators.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2010.MAR.C1.266